Free-Body Diagram

• pictures that show the size and direction of all forces acting on an object.

1. Pick one object to analyze
2. Draw a box/point to represent the object
3. Draw an arrow to represent each force acting on the object.
4. Make sure the arrow shows the direction and relative size of the force.

• a type of force.
• also known as air drag or aerodynamic drag, is a force that opposes the motion of an object through the air.
• think of it as friction but against gravity except it also works horizontally but its only for complex problems.

Formula: \(F_{air} = -kv^2\)

• \(k\) is a constant that depends on the object's shape and other factors.
• \(v\) is the object's velocity.

• It is the sum of vertical forces acting on the object.
• In static equilibrium, the sum of vertical forces is zero, meaning the normal force and weight balance each other.
• \(\sum\vec{F_y} = F_n - w = 0\) (for static equilibrium)
  • \(\sum\vec{F}_y\) represents the sum of vertical forces.
  • \(F_n\) is the normal force exerted by a supporting surface.
  • \(w\) is the weight of the object due to gravity.
• \(\sum\vec{F}_y = N + P_y - w = 0\)
  • More detailed version of the first formula.
  • \(\sum\vec{F}_y\) represents the sum of vertical forces.
  • \(N\) is the normal force exerted by a supporting surface.
  • \(P_y\) is any vertical force component applied to the object.
  • \(w\) is the weight of the object due to gravity.

• It is the sum of horizontal forces acting on the object.
• For horizontal equilibrium, the applied force and friction should balance each other out.
• \(\sum\vec{F_x} = F_a - f\)
  • \(\sum\vec{F_x}\) represents the sum of horizontal forces.
  • \(F_a\) is an applied force externally acting horizontally.
  • \(f\) represents friction, which opposes motion.
  • If pulling force \(F_a < friction\ f\) then furniture is at rest otherwise it will move to the right.
• \(\sum\vec{F}_x = P_x - f\)
  • \(P_x\) is any horizontal force component applied to the object.

• The net external force acting on the object.
• The net external force determines the object's acceleration or state of rest. If it's zero, the object is in equilibrium.
• \(\sum\vec{F} = F_{ax} - f\) where \(\vec{F}\) is the net external force
  • \(\sum\vec{F}\) represents the net external force.
  • \(F_{ax}\) is the net applied force in the horizontal direction.
  • \(f\) represents friction.
• \(\sum\vec{F} = P_x - f\)
  • \(P_{x}\) is the net applied force in the horizontal direction.
  • If \(\sum\vec{F}_y \neq 0\) then the object didn't touch the ground surface. Therefore, the net external force is \(\neq \sum\vec{F}_x\)

• Static friction is the friction force when two surfaces in contact do not move against each other, in other words it is the friction force at rest.
• if the applied force \(F_{a}\) exceeds the maximum static frictional force \(f_s\), then the object will finally move in the direction of the applied force.
• Scalar only.
• \(f_s = \mu_s\eta\)
  • \(f_s\) - maximum static friction force
  • \(\mu_s\) - coefficient of static friction
  • \(\eta\) - symbol's name is eta magnitude of normal force.
• \(\mu \propto f\)
• \(f_s \propto F_n\)

• Once an object is in motion, kinetic friction opposes the ongoing motion between the two surfaces.
• \(f_k = \mu_k\eta\)
  • \(f_k\) - kinetic friction
  • \(\mu_k\) - coefficient of kinetic friction
  • \(\eta\) - symbol's name is eta is the normal force.
• always \(f_k < f_s\)